Double search user group selection scheme with range reduction for FDD multiuser MIMO downlink transmission with finite-rate channel state information feedback

ABSTRACT

Aspects of a double search user group selection scheme with range reduction for FDD multiuser MIMO downlink transmission with finite-rate channel state information feedback are provided. The method may comprise maximizing system capacity using feedback information for a plurality of signals in a frequency division duplex system to reduce a search range within which a group of signals having maximum channel gain are located. The feedback information may comprise quantized gain for the signals. Quantized channel direction for the signals within the reduced search range may be requested and received by the transmitter. One or two signals from the reduced search range that maximizes system capacity may be selected. The receivers associated with these signals may then be selected as the user group.

CROSS-REFERENCE TO RELATED APPLICATIONS/INCORPORATION BY REFERENCE

This application makes reference to:

U.S. application Ser. No. ______(Attorney Docket No. 17021US01) filed Sep. 21, 2005;

U.S. application Ser. No. ______(Attorney Docket No. 17022US01) filed Sep. 21, 2005;

U.S. application Ser. No. ______(Attorney Docket No. 17023US01) filed Sep. 21, 2005;

U.S. application Ser. No. ______(Attorney Docket No. 17024US01) filed Sep. 21, 2005;

U.S. application Ser. No. ______(Attorney Docket No. 17025US01) filed Sep. 21, 2005;

U.S. application Ser. No. ______(Attorney Docket No. 17027US01) filed Sep. 21, 2005;

U.S. application Ser. No. ______(Attorney Docket No. 17028US01) filed Sep. 21, 2005;

U.S. application Ser. No. ______(Attorney Docket No. 17029US01) filed Sep. 21, 2005; and

U.S. application Ser. No. ______(Attorney Docket No. 17030US01) filed Sep. 21, 2005.

Each of the above stated application is hereby incorporated by reference in its entirety.

FIELD OF THE INVENTION

Certain embodiments of the invention relate to mobile communication systems. More specifically, certain embodiments of the invention relate to a method and system for a double search user group selection scheme with range reduction for FDD multiuser MIMO downlink transmission with finite-rate channel state information

feedback.

BACKGROUND OF THE INVENTION

Mobile communications have changed the way people communicate and mobile phones have been transformed from a luxury item to an essential part of every day life. The use of mobile phones is today dictated by social situations, rather than hampered by location or technology. While voice connections fulfill the basic need to communicate, and mobile voice connections continue to filter even further into the fabric of every day life, the mobile Internet is the next step in the mobile communication revolution. The mobile Internet is poised to become a common source of everyday information, and easy, versatile mobile access to this data will be taken for granted.

Third generation (3G) cellular networks have been specifically designed to fulfill these future demands of the mobile Internet. As these services grow in popularity and usage, factors such as cost efficient optimization of network capacity and quality of service (QoS) will become even more essential to cellular operators than it is today. These factors may be achieved with careful network planning and operation, improvements in transmission methods, and advances in receiver techniques. To this end, carriers need technologies that will allow them to increase downlink throughput and, in turn, offer advanced QoS capabilities and speeds that rival those delivered by cable modem and/or DSL service providers.

In order to meet these demands, communication systems using multiple antennas at both the transmitter and the receiver have recently received increased attention due to their promise of providing significant capacity increase in a wireless fading environment. These multi-antenna configurations, also known as smart antenna techniques, may be utilized to mitigate the negative effects of multipath and/or signal interference on signal reception. It is anticipated that smart antenna techniques may be increasingly utilized both in connection with the deployment of base station infrastructure and mobile subscriber units in cellular systems to address the increasing capacity demands being placed on those systems. These demands arise, in part, from a shift underway from current voice-based services to next-generation wireless multimedia services that provide voice, video, and data communication.

The utilization of multiple transmit and/or receive antennas is designed to introduce a diversity gain and to raise the degrees of freedom to suppress interference generated within the signal reception process. Diversity gains improve system performance by increasing received signal-to-noise ratio and stabilizing the transmission link. On the other hand, more degrees of freedom allow multiple simultaneous transmissions by providing more robustness against signal interference, and/or by permitting greater frequency reuse for higher capacity. In communication systems that incorporate multi-antenna receivers, a set of M receive antennas may be utilized to null the effect of (M−1) interferers, for example. Accordingly, N signals may be simultaneously transmitted in the same bandwidth using N transmit antennas, with the transmitted signal then being separated into N respective signals by way of a set of N antennas deployed at the receiver. Systems that utilize multiple transmit and receive antennas may be referred to as multiple-input multiple-output (MIMO) systems. One attractive aspect of multi-antenna systems, in particular MIMO systems, is the significant increase in system capacity that may be achieved by utilizing these transmission configurations. For a fixed overall transmitted power, the capacity offered by a MIMO configuration may scale with the increased signal-to-noise ratio (SNR). For example, in the case of fading multipath channels, a MIMO configuration may increase system capacity by nearly M additional bits/cycle for each 3-dB increase in SNR.

The widespread deployment of multi-antenna systems in wireless communications has been limited by the increased cost that results from increased size, complexity, and power consumption. This poses problems for wireless system designs and applications. As a result, some initial work on multiple antenna systems may be focused on systems that support single user point-to-point links. Recently, much attention has been focused on utilizing the multi-antenna techniques to a multiuser environment to improve throughput. Multiuser communication systems that employ multiple antennas at the base station may greatly improve the downlink system capacity. The capacity improvement is attained by communicating simultaneously to multiple users through preceding at the transmitter when channel state information (CSIT) is available. A zero-forcing (ZF) linear precoder may achieve the theoretical system sum capacity when the number of users, K, approaches infinity. However, it is not feasible to realize a system in which the number of users approaches infinity.

Further limitations and disadvantages of conventional and traditional approaches will become apparent to one of skill in the art, through comparison of such systems with some aspects of the present invention as set forth in the remainder of the present application with reference to the drawings.

BRIEF SUMMARY OF THE INVENTION

A system and/or method is provided for a double search user group selection scheme with range reduction for FDD multiuser MIMO downlink transmission with finite-rate channel state information feedback, substantially as shown in and/or described in connection with at least one of the figures, as set forth more completely in the claims.

These and other advantages, aspects and novel features of the present invention, as well as details of an illustrated embodiment thereof, will be more fully understood from the following description and drawings.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

FIG. 1A is a top-level block diagram illustrating an exemplary multiuser multiple-input-multiple-output (MIMO) downlink transmission system with linear preceding, in accordance with an embodiment of the invention.

FIG. 1B is a diagram illustrating exemplary communication between the base station and the receivers of FIG. 1A, in accordance with an embodiment of the invention.

FIG. 2A is a flow diagram illustrating exemplary steps in a double search algorithm for user group selection, in accordance with an embodiment of the invention.

FIG. 2B is a flow diagram illustrating exemplary steps in user pair selection in a double search algorithm for user group selection, in accordance with an embodiment of the invention.

FIG. 2C is a flow chart that illustrates exemplary steps in a method for a range reduction scheme for user selection in a multiuser MIMO downlink transmission, in accordance with an embodiment of the invention.

FIG. 3A is a flow diagram illustrating exemplary steps taken by base station for user group selection, in accordance with an embodiment of the invention.

FIG. 3B is a flow diagram illustrating in detail exemplary step 310 taken by base station for user group selection, in accordance with an embodiment of the invention.

FIG. 4 is a graph that illustrates exemplary downlink transmission schemes in terms of sum rate, in accordance with an embodiment of the invention.

FIG. 5 is a graph that illustrates exemplary downlink transmission schemes in terms of bit error rate, in accordance with an embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Certain embodiments of the invention may be found in a method and system for a double search user group selection scheme with range reduction for FDD multiuser MIMO downlink transmission with finite-rate channel state information feedback. Aspects of the method may comprise maximizing system capacity using feedback information for a plurality of signals in a frequency division duplex (FDD) system to reduce a search range within which a group of signals having maximum channel gain are located. The feedback information may comprise quantized gain and/or direction for the signals.

U.S. application Ser. No. ______(Attorney Docket No. 17028US01) filed on Sep. 21, 2005 provides a method and system for greedy user group selection with range reduction for FDD multiuser MIMO downlink transmission with finite-rate channel state information feedback. In this regard, a greedy user group selection with range reduction for maximizing system capacity is provided by that application. The present application discloses using a double search user group selection with range reduction for maximizing system capacity.

FIG. 1A is a top-level block diagram illustrating an exemplary multiuser multiple-input-multiple-output (MIMO) downlink transmission system with linear precoding, in accordance with an embodiment of the invention. Referring to FIG. 1A, there is shown a communication system 100 that may comprise a base station 102 a and a plurality of users 102 b, . . . , 102 c. In the communication system 100, the base station 102 a may be equipped with M antennas and K users 102 b, . . . , 102 c may each have a single antenna. In this implementation, the total number of users or receiver antennas may be equal to or higher than the number of base station antennas, that is, K≧M.

The base station 102 a may comprise a plurality of channel encoders 104 a, . . . , 104 b, a range reduction algorithm block 106, a user scheduler 108 a, a plurality of modulators (MOD) 110 a, . . . , 112 a, a power control block 114 a, a beamforming or linear precoding block 116 a, a processor 144, and a memory 146. Each of the plurality of users 102 b, . . . , 102 c may comprise one of a plurality of demodulators (DEM) 118 a, 128 a, one of a plurality of channel decoders 120 a, . . . , 130 a, one of a plurality of channel estimators 122 a, . . . , 132 a, one of a plurality of feedback controllers 124 a, . . . , 134 a, and one of a plurality of channel quantizers 126 a, . . . , 136 a.

The channel encoders 104 a, . . . , 104 b may comprise suitable logic, circuitry, and/or code that may be adapted to encode binary data for each of the K users in the communication system 100. The range reduction algorithm block 106 may comprise suitable logic, circuitry, and/or code that may be adapted to reduce a search range within which a group of signals having maximum channel gain are located. The beamforming or linear preceding block 116 a may comprise suitable logic, circuitry, and/or code that may be adapted to processes the user data symbols to separate signals intended for different users such that each of the users receives little or no interference from other users. With M antennas at the base station 102 a, the beamforming or linear preceding block 116 a may separate at most M different signals, that is, the base station 102 a may transmit to at most M users at a time. Therefore, for each channel realization, the base station 102 a may need to select M or less than M users among all the K users to transmit.

The user scheduler 108 a may comprise suitable logic, circuitry, and/or code that may be adapted to find a best user group that optimizes certain performance criterion such as the sum throughput of the system, for example. In this regard, the user scheduler 108 a may be adapted to perform the steps of a double search user selection algorithm to find the best user group. The user scheduler 108 a may be adapted to determine a first maximum system capacity based on the first user and a second maximum system capacity based on the second user. The user scheduler 108 a may also be adapted to select the highest of the first maximum system capacity and the second maximum system capacity as the maximum system capacity to be supported by the communication system 100. In this regard, for a case when M=2, the user scheduler 108 a may select a user group comprising a pair of users associated with the maximum system capacity selected.

The modulators 110 a, . . . , 112 a may comprise suitable logic, circuitry, and/or code that may be adapted to modulate the binary data of each of the users selected by the user scheduler 108 a. In this regard, the modulation operation on the binary data may result in a plurality of complex symbols, for example. The power control block 114 a may comprise suitable logic, circuitry, and/or code that may be adapted to allocate different users with different power levels in accordance with their respective channel quality, for example. The user scheduler 108 a, the power control block 114 a, and/or the beamforming or linear precoding block 116 may require knowledge of the state of the downlink channel.

The processor 144 may comprise suitable logic, circuitry, and/or code that may be adapted to process information and/or data associated with the generation of transmission signals at the base station 102 a. The processor 144 may also be adapted to control at least a portion of the operations of the base station 102 a. For example, the processor 144 may determine whether to handoff a mobile user to another base station. The memory 146 may comprise suitable logic, circuitry, and/or code that may be adapted to store data and/or control information that may be utilized in the operation of at least a portion of the base station 102 a.

The demodulators 118 a, . . . , 128 a in the users 102 b, . . . , 102 c may comprise suitable logic, circuitry, and/or code that may be adapted to demodulate the signals received from the base station 102 a, for example. The channel decoders 120 a, 130 a may comprise suitable logic, circuitry, and/or code that may be adapted to decode the demodulated signals from the demodulators 118 a, . . . , 128 a into binary bit streams, for example. The channel estimators 122 a, . . . , 132 a may comprise suitable logic, circuitry, and/or code that may be adapted to produce a channel estimate for the signal transmitted by, for example, the base station 102 a. The channel quantizers 126 a, . . . , 136 a may comprise suitable logic, circuitry, and/or code that may be adapted to quantize the channel estimate from, for example, the channel estimators 122 a, . . . , 132 a to discrete values. This may have the effect of rounding the channel estimates to a small number of quantized values. The feedback controller 124 a, . . . , 134 a may comprise suitable logic, circuitry, and/or code that may be adapted to generate a feedback signal to, for example, the base station 102 a from the channel estimates from the channel estimators 122 a, . . . , 132 a and the quantized channel estimates from the channel quantizers 126 a, . . . , 136 a.

FIG. 1B is a diagram illustrating exemplary communication between the base station and the receivers of FIG. 1A, in accordance with an embodiment of the invention. There is shown a base station 170, a first user (user 1) 160, and a second user (user 2) 162. The base station 170 may comprise antennas 172, 174, 176, and 178. The operation of the base station 170 may be substantially similar to the operation of the base station 102 a described in FIG. 1A. The operation of the first user 160 and the second user 162 may be substantially similar to the operation of users 102 b, 102 c in FIG. 1A. In this regard, the first user 160 and the second user 162 may each have a single antenna.

In this instance, the base station 170 may transmit signals 161 b and 163 b, for example, and the first user 160 may transmit a feedback signal 161 a and the second user 162 may transmit a feedback signal 163 a. The signal 161 b may be intended to be received by the first user 160.

When the base station 170 is equipped with M antennas and there are K users where each user has a single antenna, the signal model may be expressed as $\begin{matrix} {\begin{bmatrix} \gamma_{1} \\ \gamma_{2} \\ \vdots \\ \gamma_{K} \end{bmatrix} = {{\begin{bmatrix} h_{1} \\ h_{2} \\ \vdots \\ h_{K} \end{bmatrix}x} + n}} & (1) \end{matrix}$ where γ_(κ)(κ=1, . . . ,K) is the signal received by user κ,h_(κ)ε℄^(1×M) is the channel vector to user k, x ε℄^(M×1) is the transmitted symbol vector by the base station 170, and n ε℄^(K×1) is the additive white Gaussian noise (AWGN) with zero mean and unit variance. The transmitted symbols may satisfy certain power constraint, for example E[x^(H)x]≦P, where (•)^(H) represents complex conjugate transpose.

In this exemplary analysis, each element in h_(k) may be a zero-mean circularly symmetric complex Gaussian (ZMCSCG) random variable with unit variance. Moreover, the users may experience independent fading and therefore the channel vectors {h_(k)}_(k=1) ^(K) may be statistically independent from each other. The channel state information (CSI), h_(k) may be known to user k, but may not be known to other users. The base station 170 may have knowledge of the CSI for all users. This may occur for a frequency division duplex (FDD) system where CSI feedback may be received by the base station 170 from the users.

Employing multiple antennas at the base station in cellular multiuser communication systems may improve the downlink system capacity. This approach may be utilized with any multiuser MIMO system, such as CDMA2000, WCDMA, and Wireless LAN (WLAN), for example. The capacity improvement may be attained by communicating simultaneously to multiple users through precoding at the transmitter or base station when channel state information is available. In this regard, a transmitter or base station may refer to any device or equipment that may be adapted to communicate with multiple other devices, users, and/or receivers. Moreover, user or receiver may refer to user device and/or equipment that may be adapted for communication with a base station and/or other devices. Dirty paper coding (DPC) may be utilized as a precoding scheme that may achieve the sum capacity, however, it may be difficult to implement due to complexity issues. There may also exist other suboptimal but relatively low complexity schemes for multiuser MIMO downlink, such as linear preceding, Tomlinson-Harashima preceding, and vector encoding, for example.

Recently, it has been shown that zero-forcing (ZF) linear precoder may achieve the sum capacity when combined with infinite-order multiuser diversity, that is, when the number of users K approaches infinity. Moreover, ZF precoders may provide near-optimal performance even with a limited number of users, when K=10 for example.

Zero-forcing precoders may be a specific type of linear precoders. When the base station, for example the base station 102 a in FIG. 1A, decides to transmit to a group of users D ⊂{1, . . . , K} with d=|D|≦K a linear precoding scheme linearly weighs the data symbols, S=[S₁, . . . , S_(d)]^(T) before they are transmitted from the base station, x=FPs,  (2) where x is the transmitted signal vector as in equation (1), F=[f₁, . . . ,f_(d)] is the M×d linear precoding matrix with normalized columns (∥f_(k)∥=1), and P=diag {P₁, . . . , P_(d)} with ${\sum\limits_{i = 1}^{d}P_{i}} \leq P$ is the power control matrix that allocates transmit power to the different users. The data symbols s may correspond to the data symbols u₁ . . . u_(M) that are generated by the plurality of modulators 110 a . . . 112 a. The elements in the linear precoding matrix F may represent the plurality of weighing coefficients utilized by the precoder 116 a. The nonzero elements in the diagonal matrix P may represent the plurality of scaling factors p₁ . . . p_(M) utilized by the power control block 114 a. The received signal may be given by: $\begin{matrix} {\begin{bmatrix} \gamma_{1} \\ \gamma_{2} \\ \vdots \\ \gamma_{d} \end{bmatrix} = {{\begin{bmatrix} h_{1} \\ h_{2} \\ \vdots \\ h_{d} \end{bmatrix}\quad{FPs}} + {n.}}} & (3) \end{matrix}$

A zero-forcing precoder may utilize a pseudo-inverse of the overall channel matrix H_(D)={h₁ ^(T), . . . , h_(d) ^(T)}^(T) as the weighting matrix when H_(D) may have full row rank according to the following equation: $\begin{matrix} {{W_{D} = {H_{D}^{\dagger} = {H_{D}^{H}\left( {H_{D}H_{D}^{H}} \right)}^{- 1}}},} & (4) \\ {{F_{D} = {W_{D}\begin{bmatrix} \frac{1}{w_{1}} & \quad & \quad \\ \quad & ⋰ & \quad \\ \quad & \quad & \frac{1}{w_{d}} \end{bmatrix}}},} & (5) \end{matrix}$ where {w_(i)}_(i=1) ^(d) dare the columns of W_(D). By defining $\begin{matrix} {\xi_{i}\overset{\Delta}{=}\frac{1}{w_{i}}} & (6) \end{matrix}$ and substituting equation (5) into equation (3), the received signal for each user with zero-forcing precoding may be expressed as, γ_(i)=ξ_(i) P _(i) s _(i) +n _(i) , ∀i εD.  (7)

In this regard, the multiuser downlink channel may become a set of parallel channels. The maximum sum rate of the given user group D may be given by the following expression: $\begin{matrix} {{C_{D} = {\sum\limits_{i \in D}{\log\left( {1 + {\xi_{i}P_{i}}} \right)}}},} & (8) \end{matrix}$ where the optimal P_(i) is given by the water-filling solution, $\begin{matrix} {{P_{i} = \left( {\mu - \frac{1}{\xi_{i}}} \right)^{+}},} & (9) \end{matrix}$ with the water level μ chosen to satisfy ${\sum\limits_{i \in D}\left( {\mu - \frac{1}{\xi_{i}}} \right)^{+}} = {P.}$ The maximum achievable sum rate for a given channel realization may be obtained by searching over all the possible user groups, that is, $\begin{matrix} {C = {\max\limits_{{D \subseteq {\{{1,\ldots\quad,K}\}}},{{D} \leq M}}{C_{D}.}}} & (10) \end{matrix}$

An optimal or best user group selection for ZF preceding may require searching over all $\sum\limits_{i = 1}^{M}\begin{pmatrix} K \\ i \end{pmatrix}$ candidate user groups to find the one with the largest sum rate, which leads to a fairly high computational cost. Moreover, in an FDD system, all the channel state information that may be needed at the transmitter to perform the optimal user group search may be obtained from the users through a feedback link, for example, the feedback link 142 a. Because the optimal search requires CSI from each user and each user's channel is a complex vector of dimension M, that is equivalent to 2M real numbers per user, heavy burden may be placed on the feedback link 142 a to obtain this information. This may be particularly cumbersome since the feedback link 142 a may tend to have very limited capacity. A user group selection scheme that results in a simpler implementation and requires less feedback information may be very useful in multiuser communication systems with multiple transmit antennas.

FIG. 2A is a flow diagram illustrating exemplary steps in a double search algorithm for user group selection, in accordance with an embodiment of the invention. Referring to FIG. 2A, there is shown a flow diagram 200 that may correspond to a double search algorithm for user group selection for a communication system where the transmitter is equipped with M=2 antennas. In this regard, the communication system supported by the flow diagram 200 may be a third-generation cellular communication system, such as WCDMA and CDMA200, where two antennas may be typically employed at the base station.

In step 210, after start step 202, the ideal channel state information (CSI) may be available at the base station 102 a, for example, via the feedback link 142 a. In this regard, the multiple-input-single-output (MISO) channel impulse response h_(k)ε℄^(1×2)(M=2) of each of the K users 102 b, . . . , 102 c may be known at the base station 102 a. The strongest user, represented by the index i, may be selected based on the maximum of the channel powers of all the K users 102 b, . . . , 102 c in the communication system 100, that is, $\begin{matrix} {i = {\arg\quad{\max\limits_{i \leq k \leq K}{\gamma_{k}.}}}} & (11) \end{matrix}$

In step 220, the i^(th) user determined in step 210 may be selected as a first candidate to communicate with the base station 102 a. In this regard, a first search may be performed in step 220 to determine which of the remaining users may be a second candidate for communication with the base station 102 a. In step 221, the maximum system capacity, C_(max), may be initialized to be the rate or capacity supported by having the base station 102 a communicate only with the i^(th) user selected in step 210, C _(max) =C(i)=log₂(1+ρ·γ_(i)).  (12) and the index [idx₁, idx₂] corresponding to a pair of users or receivers to communicate with the base station 102 a may be initialized to [i,0]. In step 223, a current k^(th) user may be compared to the i^(th) user selected in step 210. When the k^(th) user is the same as the i^(th) user, the search for a second candidate may proceed to step 228. When the k^(th) user is different from the i^(th) user the search for a second candidate may proceed to step 225.

In step 225, the system capacity of communicating to user pair (i,k) may be calculated by the following expression: $\begin{matrix} {{{C\left( {i,k} \right)} = {{\log_{2}\left( {1 + {\frac{1}{2}{\rho \cdot \gamma_{i} \cdot a_{i,k}}}} \right)} + {\log_{2}\left( {1 + {\frac{1}{2}{\rho \cdot \gamma_{\kappa} \cdot a_{i,k}}}} \right)}}},} & (13) \end{matrix}$ where ρ is the average signal-to-noise ratio (SNR) of the system, and α_(i,k) is a parameter that describes the orthogonality between h_(i) and h_(k), $\begin{matrix} {\alpha_{i,k} = {1 - {\frac{{\left\langle {h_{i},h_{k}} \right\rangle }^{2}}{{h_{i}}^{2} \cdot {h_{k}}^{2}}.}}} & (14) \end{matrix}$ The system capacity in equation (13) may be compared to the maximum system capacity C_(max) obtained thus far. When the system capacity determined in step 225 is lower than the current maximum system capacity, the process may proceed to step 228. When the system capacity determined in step 225 is higher than the current maximum system capacity, the process may proceed to step 227. In step 227, the maximum capacity C_(max) may be updated and the corresponding user pair index [i, k] may be stored.

In step 228, the current user is compared to the total number of users, K, to determine whether the search has exhausted all possible second candidates for communication with the base station 102 a. If the search has been exhausted, the process may proceed to step 230. If the search has not been exhausted, the process may proceed to step 229 where the user index value may be increased by one. After step 229, the process may proceed back to step 223 to compare the current (k+1)^(th) user to the i^(th) user selected in step 210.

In step 230, a second strongest user, represented by the index j, or j^(th) user, may be selected from the users that remain after the user with the strongest channel power has been selected. In this regard, the second strongest user may be selected based on the following expression: $\begin{matrix} {j = {\arg\quad{\max\limits_{k \neq i}\quad{\gamma_{k}.}}}} & (15) \end{matrix}$

In step 240, the j^(th) user determined in step 230 may be selected as a first candidate to communicate with the base station 102 a. In this regard, a second search may be performed in step 240 to determine which of the remaining users may be a second candidate for communication with the base station 102 a. In step 241, the current second candidate or user, represented by the index k, may be initialized to k=1, that is, the index [idx₁, idx₂] corresponding to a pair of users or receivers to communicate with the base station 102 a may be initialized to [i, 1]. In this regard, the maximum system capacity, C_(max), may correspond to the maximum system capacity determined in step 227.

In step 243, a current k^(th) user may be compared to the i^(th) and j^(th) user devices selected in steps 210 and 230 respectively. When the k^(th) user is the same as either the j^(th) user or the i^(th) user, the search for a second candidate may proceed to step 248. When the k^(th) user is different from the j^(th) user or the i^(th) user, the search for a second candidate may proceed to step 245.

In step 245, the system capacity of communicating to user pair (j,k) may be calculated by using equation (13). The system capacity in equation (13) may be compared to the maximum system capacity C_(max) obtained so far. When the system capacity determined in step 245 is lower than the current maximum system capacity, the process may proceed to step 248. When the system capacity determined in step 245 is higher than the current maximum system capacity, the process may proceed to step 247. In step 247, the maximum capacity C_(max) may be updated and the corresponding user pair index [j, k] may be stored.

In step 248, the current user is compared to the total number of users, K, to determine whether the search has exhausted all possible second candidates for communication with the base station 102 a. When the search has been exhausted, the process may proceed to step 250. When the search has not been exhausted, the process may proceed to step 249 where the user index value may be increased by one. After step 249, the process may proceed back to step 243 to compare the current (k+1)^(th) user to the it and j^(th) users selected in steps 210 and 230 respectively.

In step 250, the optimal user pair index [idx₁, idx₂] for communicating with the base station 102 a may be determined based on the results from the first search performed in step 220 and the second search performed in step 240.

FIG. 2B is a flow diagram illustrating exemplary steps in user pair selection in a double search algorithm for user group selection, in accordance with an embodiment of the invention. Referring to FIG. 2B, there is shown a flow diagram 203 that may correspond to a double search algorithm for user group selection for a communication system where the transmitter is equipped with M=2 antennas. The flow diagram 203 provides additional detail to step 250 in FIG. 2A while steps 210, 220, 230, and 240 may be substantially as described in FIG. 2A.

In step 210, a first candidate for communication with the base station 102 a may be selected for a first optimal user group selection search based on the maximum of the channel powers of all the K users 102 b, . . . , 102 c in the communication system 100 as described by equation (11). In step 220, a second candidate for communication with the base station 102 a may be determined based on the maximum capacity that may be achieved for a user pair that comprises the first candidate selected in step 210. The user pair associated with the maximum capacity may be stored. In step 230, a first candidate for communication with the base station 102 a may be selected for a first optimal user group selection search based on the maximum of the channel powers of all the remaining K users 102 b, . . . , 102 c in the communication system 100 as described by equation (15). In step 240, a second candidate for communication with the base station 102 a may be determined based on the maximum capacity that may be achieved for a user pair that comprises the first candidate selected in step 230.

After step 240, in step 252, the maximum capacity determined in step 220 may be compared to the maximum capacity determined in step 240. When the maximum capacity determined in step 220 is the greater of the two, the process may proceed to step 254. In step 254, the user pair index [idx₁, idx₂]=[i, k] associated with the maximum capacity determined in step 220 may be utilized by the base station 102 a for transmission. Returning to step 252, when the maximum capacity determined in step 240 is the greater of the two, the process may proceed to step 256. In step 256, the user pair index [idx₁, idx₂]=[j, k] associated with the maximum capacity determined in step 240 may be utilized by the base station 102 a for transmission.

The U.S. application Ser. No. ______(Attorney Docket No. 17023US01) provides a detailed description of the double search algorithm for user group selection, described in part in flow diagrams of FIGS. 2A and 2B, and is hereby incorporated herein by reference in its entirety.

In addition to maintaining very low computational complexities, various embodiments of the invention may require very low CSI feedback rate, for example, on the order of a few bits. The user selection algorithm may combine the double search user selection algorithm, which may be used by the User Scheduler 108 a, and the range reduction algorithm that specifies a reduced/smaller user range within which the scheduler searches for the best user group. The User Scheduler 108 a, the Power Controller 114 a, and the Linear Precoder block 116 a may require knowledge of the state of the downlink channel. In a frequency division duplex (FDD) system, the base station may have to obtain the downlink channel state information through a finite-rate feedback link, for example, the feedback link 142 a, from the users, for example, the users 102 b, . . . , 102 c. Each user may estimate its own channel and quantize the channel according to the feedback rate constraint. Then the feedback controller 124 a or 134 a at each user may decide what information to feed back on the request of the base station 102 a.

Since two antennas may be employed in the main third-generation cellular communication standards, such as WCDMA and CDMA2000, the number of antennas used may be two (M=2). However, the various embodiments of the invention may be utilized for any value of M.

FIG. 2C is a flow chart that illustrates exemplary steps in a method for a range reduction scheme for user selection in a multiuser MIMO downlink transmission, in accordance with an embodiment of the invention. Referring to FIG. 2, in step 270, channel state information (CSI) may be derived, step 272 comprise a search for optimal users, step 274 may comprise computing a cumulative distribution function (CDF) among user indexes, and step 276 may comprise computing a reduced search range.

In step 270 CSI may be derived based on a plurality of T independent channel realizations, for example: {h _(k)(t)}_(k=1) ^(K) , t=, . . . ,T.  (16)

The CSI may comprise channel gain, or signal gain, information. For each channel realization, users among the full set of K users may be sorted, and indexed, in an order based on the values of the channel gains corresponding to each of the K users. For example, a user with a larger value of corresponding channel gain may be placed in the sorted list at a higher index than a user with a smaller value of corresponding channel gain as in the following expression: $\begin{matrix} {{{\gamma_{1}(t)} \geq {\gamma_{2}(t)} \geq \ldots\quad \geq {\gamma_{K}(t)}},{t = 1},\ldots\quad,T,\quad{where}} & (17) \\ {{\gamma_{k}(t)}\overset{\Delta}{=}{{{h_{k}(t)}}^{2}.}} & (18) \end{matrix}$

The channel measurement may be carried out either by offline channel sounding or by online channel estimation. In a FDD system, the downlink CSI may be estimated by the users 102 b, . . . , 102 c and subsequently communicated to the base station 102 a via a dedicated feedback link 142 a.

In step 272, for each of the channel realizations according to (16), the optimal user group may be determined according to (8) and (10) as in the following expression: $\begin{matrix} {{{D_{opt}(t)} = {\arg\quad{\max\limits_{{D \subseteq {\{{1,\ldots\quad,K}\}}},{{D} \leq M}}{C_{D}(t)}}}},{t = 1},\ldots\quad,T,{where}} & (19) \\ {{{C_{D}(t)} = {\sum\limits_{i \in D}{\log\left( {1 + {{\xi_{i}(t)}{P_{i}(t)}}} \right)}}},} & (20) \end{matrix}$ and where ξ₁(t) and P_(i)(t) may be as defined in equations (6) and (9), respectively. D_(opt)(t) may be represented as a row vector that contains indexes corresponding to the users 102 b, . . . , 102 c contained in the optimal group for channel realization ι. By representing the index of the optimal users as a random variable X, the vector as in the following expression: $\begin{matrix} {D_{opt}\overset{\Delta}{=}\left\lbrack {{D_{opt}(1)},{D_{opt}(2)},\ldots\quad,{D_{opt}(T)}} \right\rbrack} & (21) \end{matrix}$ may contain samples of the random variable X.

In step 274, an estimate of the cumulative distribution function (CDF) {circumflex over (F)}(X) of X may be produced based on samples from the optimal user index vector, X, that was determined in step 272 according to equation (21).

In step 276, a threshold, δ_(th)ε(0,1], may be selected. The reduced search range then be determined by the relationship as in the following expression: L={circumflex over (F)} ⁻¹(δ_(th))  (22) where {circumflex over (F)}⁻¹(•) is the inverse function of {circumflex over (F)}(•), for example: X={circumflex over (F)} ⁻¹({circumflex over (F)}(X))  (23) The threshold may be a measure of the likelihood that the channel realization, evaluated among the full range of K users, will comprise the subset of L users.

In various embodiments of the invention, expression (22) may be implemented by tabulating the CDF {circumflex over (F)}(X) in terms of the random variable comprising the index of optimal users X, and searching for a value of X that corresponds to δ_(th) The threshold δ_(th) may provide a measure of the statistical likelihood that the sum rate, computed among of subset of L users in the reduced searching range, may approach the optimal performance computed among the full group of K users.

The U.S. application Ser. No.______ (Attorney Docket No. 17024US01) provides a detailed description of the range reduction algorithm for user group selection, described in part in flow diagram of FIG. 2C, and is hereby incorporated herein by reference in its entirety.

While the exemplary embodiment of the invention illustrates a search range reduction scheme a system that utilizes a simple zero-forcing precoder, the invention is not so limited. Various embodiments of the invention may also be utilized with other more sophisticated precoders, for example a minimum mean squared error (MMSE) precoder, a Tomlinson-Harashima precoding (THP) precoder, or a sphere encoding precoder, for example.

FIG. 3A is a flow chart illustrating exemplary steps for user group selection, in accordance with an embodiment of the invention. Referring to FIG. 3 a, in step 302, the range reduction algorithm may be applied to find the reduced user search range L. Thus, the L strongest users may need to be searched to find a desired user group. An embodiment of the invention may use an offline-calculated user range as the initial value while updating L at real time with online channel measurements.

It may be assumed that users have ideal channel state information available to receiver (CSIR) such that the multiple input single output (MISO) channel impulse response h_(k)ε℄^(1×2)(M=2) may be perfectly known at each user. In step 304, each user may quantize its own channel gain (or channel power) γ_(k)=∥h_(k)∥² by a finite-rate scalar quantizer with quantization resolution B_(g) bits per channel update. The quantized channel gain {circumflex over (γ_(k))}, or the equivalent quantization index, may then be conveyed back to the base station 102 a through a rate constrained or very low bit rate feedback link 142 a. The channel gain quantizer may be optimized to match to the precoder used at the transmitter, such as, for example, the zero-forcing precoder. Specific performance metric, such as capacity and bit error rate, as well channel statistical distributions, may also be taken into account so as to improve the system performance.

In step 306, based on the feedback information $\hat{\gamma_{i}}{_{i = 1}^{K},}$ all the users may be sorted and indexed in terms of their channel gains, $\begin{matrix} {\hat{\gamma_{i}} \geq \hat{\gamma_{2}} \geq \ldots \geq {\hat{\gamma_{K}}.}} & (24) \end{matrix}$ Further based on the obtained range [1, L] from step 302, the base station 102 a may request the first L strongest users to send back their channel direction v_(i)=h_(i)/∥h_(i)∥.

In step 308, based on the request from the base station 102 a, for 1≦i≦L, the i^(th) user may quantize its own channel direction by a vector quantizer with inner product quantization criterion. The direction vector v_(i) may hence be quantized into {circumflex over (v)}_(i) with quantization resolution B_(v) bits per channel update. The quantized vector {circumflex over (v)}_(i) or the quantization index, may be fed back to the base station 102 a using the feedback link 142 a.

In step 310, the first L strongest users may be searched based on the feedback channel information v̂_(i)_(i = 1)^(L)  and  γ̂_(i)_(i = 1)^(L) for a user pair [idx₁, idx₂] that may have the maximum instantaneous sum capacity. According to the double search algorithm described with respect to FIGS. 2A and 2B, the first candidate of the user pair may be restricted to be the first and second strongest users (user 1 and user 2). Step 310 is described in more detail with regard to FIG. 3B. $F = {\left\lbrack {{\hat{v}}_{{idx}\quad 2}^{\bot H}{\hat{v}}_{{idx}\quad 1}^{\bot H}} \right\rbrack/{\sqrt{2}.}}$

In step 312, based on the result of the search process in step 310, an optimal user pair index [idx₁, idx₂] may be obtained. There may be two cases for the indices obtained. In the first case, if both idx₁ and idx₂ are valid indices between 1 and K, then the base station 102 a may communicate to both user idx₁ and user idx₂ at the same time utilizing spatial multiplexing. The transmitter preceding matrix F may be generated using the following expression: F=[{circumflex over (v)} _(idx2) ^(⊥H) {circumflex over (v)} _(idx1) ^(⊥H)]/√{square root over (2)}.  (25) which may be equivalent to the form given by equation (5).

In the second case, if idx₂ is equal to 0, this means that communicating only to the strongest user, for example the user with index idx₁, may provide better sum capacity than using spatial multiplexing. In this case, the preceding matrix F may be chosen to be F={circumflex over (v)} _(idx1) ^(H).  (26)

FIG. 3B is flow chart illustrating one of the exemplary steps of FIG. 3A, which is utilized for user group selection, in accordance with an embodiment of the invention. Referring to FIG. 3B, there is shown a more detailed description of step 310 of FIG. 3A comprising steps 310 a, 310 b, 310 c, 310 d, 310 e, 310 f, 310 g, and 310 h. The step 310 may use a double “for-loop” to obtain the optimal user pair. In step 310 a, the maximum system capacity C_(max) may be first initialized to C_(max)=C(1), which may correspond to the case where the base station 102 a may only transmit to the strongest user as given by the expression: C _(max) =C(1)=log₂(1+ρ·{circumflex over (γ)}₁)  (27) The optimal user index may be initialized to [idx₁, idx₂]=[1,0] with idx₂=0 indicating that there is no second user. A first count variable i may be set to 1.

The first for-loop may start with step 310 b, and may comprise steps 310 c, 310 d, 310 e, 310 f, 310 g, and 310 h. Step 310 b may increment the value of k where k may be a second count variable. In step 310 c, a system maximum sum capacity C_(max), with C(i,k) may be compared to the system maximum sum capacity C_(max), with C(i,k). The system maximum sum capacity C_(max), with C (i, k) may be given by the expression: $\begin{matrix} {{{C\left( {i,k} \right)} = {{\log_{2}\left( {{1 + {\frac{1}{2}\rho}}{\cdot {\hat{\gamma}}_{i} \cdot \alpha_{i,k}}} \right)} + {\log_{2}\left( {1 + {\frac{1}{2}{\rho \cdot {\hat{\gamma}}_{\kappa} \cdot \alpha_{i,k}}}} \right)}}}{{i = 1},{{2\quad k} = 2},\ldots\quad,L,}} & (28) \end{matrix}$ where ρ may be the average SNR of the system, and α_(i,k) may be a parameter that describes orthogonality between v_(i) and V_(k), α_(i,k)=1−|{circumflex over (v)} _(i) ,{circumflex over (v)} _(k)

|²  (29) If the system capacity C(i,k) is larger than the current maximum capacity C_(max), the next step may be step 310 d. Otherwise, the next step may be step 310 e. In this regard, the system maximum sum capacity C_(max) may correspond to the transmit data rate of the system when transmitting to either one user as indicated by [idx₁, idx₂]=[1,0] or two users as indicated by [idx₁, idx₂]=[i, k]

In step 310 d C_(max) may be updated with C(i,j) and the optimal user index [idx₁,idx₂] may updated by [i,k]. In step 310 e, the second count variable k may be compared to L. If the second count variable k is greater than L, the next step may be step 310 g, otherwise the next step may be 310 f.

In step 310 f, the second count variable k may be incremented by one, and the next step may be step 310 c. In step 310 g, the first count variable i may be compared to the value two. If the first count variable i is greater than two, the next step may be step 312 and the search may be finished. Otherwise the next step may be step 310 h and the search may continue. In step 310 h, the first count variable i may be incremented by one. The next step may be step 310 b.

The for-loop comprising the steps 310 b, 310 c, 310 d, 310 e, 310 f, 310 g, and 310 h may examine all possible user pairs [i, k] with i=1, 2 and k=2, . . . , L and at the end of the search algorithm, an optimal user pair index [idx₁, idx₂] that may result in a maximum system sum capacity.

FIG. 4 is a graph that illustrates exemplary downlink transmission schemes in terms of sum rate, in accordance with an embodiment of the invention. Referring to FIG. 4, there is shown the results of a numerical simulation corresponding to the sum rate of a cellular system with a single base station and K=100 users. The base station may be equipped with M=2 antennas, for example, and each user may be equipped with a single antenna. The channels are flat Rayleigh faded channels. The transmit antennas at the base station may be spaced or separated so as to experience independent fading. The modulation format applied may be quadrature phase-shift keying (QPSK), for example.

FIG. 4 may provide three results. The first result may be a signal 402 that may correspond to the rate sum of a brute force selection with ideal CSI at transmitter (CSIT) and a user set of 100 users. The second result may be a signal 404 that may correspond to the rate sum of the double search algorithm with 3 bits allocated for channel gain feedback (B_(g)=3), 6 bits allocated for channel directional feedback (B_(v)=6), and a reduced search range of 10 strongest users, (L=10). The third result may be a signal 406 that may correspond to the rate sum of the double search algorithm with 3 bits allocated for channel gain feedback (B_(g)=3), 6 bits allocated for channel directional feedback (B_(v)=6), and a reduced search range of 5 strongest users (L=5).

FIG. 5 is a graph that illustrates exemplary downlink transmission schemes in terms of bit error rate, in accordance with an embodiment of the invention. Referring to FIG. 5, there is shown the results of a numerical simulation corresponding to the sum rate of a cellular system with a single base station and K=100 users. The base station may be equipped with M=2 antennas, for example, and each user may be equipped with a single antenna. The channels are flat Rayleigh faded channels. The transmit antennas at the base station may be spaced or separated so as to experience independent fading. The modulation format applied may be quadrature phase-shift keying (QPSK), for example.

FIG. 5 may provide three results. The first result may be a signal 502 that may correspond to the BER of the brute force selection with ideal CSI at transmitter (CSIT) and s user set of 100 users. The second result may be a signal 504 that may correspond to the BER of the double search algorithm with 3 bits allocated for channel gain feedback (B_(g)=3), 6 bits allocated for channel directional feedback (B_(v)=6), and a reduced search range of 10 strongest users (L=10). The third result may be a signal 506 that may correspond to the BER of the double search algorithm with 3 bits allocated for channel gain feedback (B_(g)=3), 6 bits allocated for channel directional feedback (B_(v)=6), and a reduced search range of 5 strongest users (L=5).

The graphs of FIGS. 4 and 5 may indicate that the double search user selection algorithm with a reduced search range of L=10 or L=5 may provide very similar capacity and/or BER performance as the optimal brute-forcing search scheme with a full search range L=100. However, the brute-forcing search algorithm may need to search over $\frac{L\left( {L + 1} \right)}{2}$ user groups for M=2, whereas the double search algorithm may have 2L-3 user groups. This is summarized in Table 1 below. Therefore, the user selection technique may be capable of achieving near-optimal performance while significantly reducing the computational burden on the base station 102 a.

Additionally, in a frequency division duplex (FDD) system where the base station 102 a may have to obtain the CSI from the users 102 b, . . . , 102 c through the feedback link 142 a, the amount of feedback may be reduced because the base station 102 a may only need to have full knowledge of the L strongest users instead of all the k users. If, for each user's channel h_(k), B_(g) bits are used to quantize its gain ∥h_(k)∥² and B_(v), bits to quantize its direction $\frac{h_{k}}{h_{k}},$ the total amount of feedback may be given by: B=K·B _(g) +L·B _(v).  (30)

Additionally, B_(v) may be much larger than B_(g) in practical systems. Therefore, reducing L may save a significant amount of feedback needed by the base station 102 a. Table 1 gives a summary of the amount of feedback for various choices of L when B_(g)=2 bits and B_(v)=6 bits. TABLE 1 Selection Schemes M = 2, K = 100, B_(g) = 2 bits, B_(v) = 6 bits Brute Double Double Force Search Search L = 100 L = 10 L = 5 # of Candidate User Groups 5050 17 7 Feedback Amount B(bits) 800 260 230

One embodiment of the invention may comprise maximizing system capacity using feedback information for a plurality of signals to reduce a search range within which a group of signals having maximum channel gain are located. Incorporated U.S. application Ser. No. ______(Attorney Docket No. 17024US01) provides a detailed description of a method and system that may be utilized to reduce a search range within a group of signals. The search range reduction may be executed by the range reduction algorithm block 106. The group of signals may be transmitted by the users 102 b, . . . , 102 c. The feedback information may comprise quantized gain for the signals and may be fed back from the receiving user devices via the feedback link 142 a. Quantized channel information, which may comprise quantized channel direction, may be requested for the signals within the reduced search range, and the quantized channel direction may be received.

A double search may be performed in order to determine at least one user that may be utilized to maximize the system capacity. For the double search, a first signal may be selected by the user scheduler 108 a that corresponds to a channel gain that may be greater than a channel gain of other signals within the reduced search range. A second signal may be selected by the user scheduler 108 a from the remaining portion of signals within the reduced search range. The second signal may correspond to a channel gain that may be greater than the rest of the remaining portion of the signals within the reduced search range. The user scheduler 108 a may maximize system capacity based on the first signal and the second signal.

A first system capacity may be maximized based on the channel gain corresponding to the first signal. A first pair of receivers associated with the maximized first system capacity may be selected by the user scheduler 108 a. A second system capacity may be maximized based on the channel gain corresponding to the second signal. A second pair of receivers associated with the maximized first system capacity may be selected by the user scheduler 108 a. The system capacity may be maximized based on a greater of the maximized first system capacity and the maximized second system capacity. A pair of receivers that provide the maximized system capacity may then be selected. Downlink transmission by the base station 102 a may communicate data to the selected receivers.

Accordingly, the present invention may be realized in hardware, software, or a combination of hardware and software. The present invention may be realized in a centralized fashion in at least one computer system, or in a distributed fashion where different elements are spread across several interconnected computer systems. Any kind of computer system or other apparatus adapted for carrying out the methods described herein is suited. A typical combination of hardware and software may be a general-purpose computer system with a computer program that, when being loaded and executed, controls the computer system such that it carries out the methods described herein.

The present invention may also be embedded in a computer program product, which comprises all the features enabling the implementation of the methods described herein, and which when loaded in a computer system is able to carry out these methods. Computer program in the present context means any expression, in any language, code or notation, of a set of instructions intended to cause a system having an information processing capability to perform a particular function either directly or after either or both of the following: a) conversion to another language, code or notation; b) reproduction in a different material form.

While the present invention has been described with reference to certain embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the scope of the present invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the present invention without departing from its scope. Therefore, it is intended that the present invention not be limited to the particular embodiment disclosed, but that the present invention will include all embodiments falling within the scope of the appended claims. 

1. A method for processing signals in a communication system, the method comprising maximizing system capacity using feedback information for a plurality of signals in a frequency division duplex system to reduce a search range within which a group of signals having maximum channel gain are located.
 2. The method according to claim 1, wherein said feedback information comprises quantized gain for said plurality of signals.
 3. The method according to claim 2, further comprising requesting quantized channel information for signals within said reduced search range.
 4. The method according to claim 3, wherein said requested quantized channel information comprises quantized channel direction for said signals within said reduced search range.
 5. The method according to claim 1, further comprising receiving quantized channel direction for said signals within said reduced search range.
 6. The method according to claim 5, further comprising: selecting, from a plurality of signals within said reduced search range, a first signal corresponding to a channel gain that is greater than a channel gain corresponding to a remaining portion of said plurality of signals within said reduced search range; selecting, from said remaining portion of said plurality of signals within said reduced search range, a second signal corresponding to a channel gain that is greater than a channel gain corresponding to a remaining portion of said remaining portion of said plurality of signals within said reduced search range; and maximizing said system capacity based on said selected first signal and said selected second signal.
 7. The method according to claim 6, further comprising maximizing a first system capacity based on said channel gain corresponding to said selected first signal.
 8. The method according to claim 7, further comprising selecting a first pair of receivers associated with said maximized first system capacity.
 9. The method according to claim 6, further comprising maximizing a second system capacity based on said channel gain corresponding to said selected second signal.
 10. The method according to claim 9, further comprising selecting a second pair of receivers associated with said maximized first system capacity.
 11. The method according to claim 6, further comprising maximizing said system capacity based on a greater of a maximized first system capacity and a maximized second system capacity.
 12. The method according to claim 11, further comprising selecting a pair of receivers that provide said maximized system capacity.
 13. A system for processing signals in a communication system, the system comprising circuitry that maximizes system capacity using feedback information for a plurality of signals in a frequency division duplex system to reduce a search range within which a group of signals having maximum channel gain are located.
 14. The system according to claim 13, wherein said feedback information comprises quantized gain for said plurality of signals.
 15. The system according to claim 14, further comprising circuitry that requests quantized channel information for signals within said reduced search range.
 16. The system according to claim 15, wherein said requested quantized channel information comprises quantized channel direction for said signals within said reduced search range.
 17. The system according to claim 13, further comprising circuitry that receives quantized channel direction for said signals within said reduced search range.
 18. The system according to claim 17, further comprising: circuitry that selects, from a plurality of signals within said reduced search range, a first signal corresponding to a channel gain that is greater than a channel gain corresponding to a remaining portion of said plurality of signals within said reduced search range; said circuitry selects, from said remaining portion of said plurality of signals within said reduced search range, a second signal corresponding to a channel gain that is greater than a channel gain corresponding to a remaining portion of said remaining portion of said plurality of signals within said reduced search range; and said circuitry maximizes said system capacity based on said selected first signal and said selected second signal.
 19. The system according to claim 18, wherein said circuitry maximizes a first system capacity based on said channel gain corresponding to said selected first signal.
 20. The system according to claim 19, wherein said circuitry selects a first pair of receivers associated with said maximized first system capacity.
 21. The system according to claim 18, wherein said circuitry maximizes a second system capacity based on said channel gain corresponding to said selected second signal.
 22. The system according to claim 21, wherein said circuitry selects a second pair of receivers associated with said maximized first system capacity.
 23. The system according to claim 18, wherein said circuitry maximizes said system capacity based on a greater of a maximized first system capacity and a maximized second system capacity.
 24. The system according to claim 23, wherein said circuitry selects a pair of receivers that provide said maximized system capacity.
 25. The system according to claim 23, wherein said circuitry comprises at least one of the following: a scheduler and a processor. 